The fact is that economies DO RECOVER from recessions even when government provides no sort of artificial stimulus to assist the recovery: after all, economies recovered from recessions in the 1800s before the days of “artificial stimulus”. So how do free markets do it?
In very simple economies, Say’s law works well. To illustrate, Robinson Crusoe lands on island which has a few other inhabitants. Crusoe’s speciality is fishing. So he does that. The result is that the price of fish falls relative to other goods produced on the island. So demand for fish rises. Hey presto: full employment is achieved.
However, when economies get more complicated and money is introduced, there’s a problem. If there is excess saving (of money), that necessarily means money is being saved rather than being spent. And since spending money on goods and services employes people, the result of that saving is increased unemployment. Keynes called that phenomenon the “paradox of thrift”.
So how does the free market deal with that problem?
Well in a recession, there is a surplus of people who want to obtain money via work. Assuming a free market, the hourly wage of those people will decline. That will make it profitable for others (the asset rich) to take out loans (i.e. create money) using their assets as collateral and employ the unemployed to create more assets for the asset rich (cars, houses, etc).
Incidentally for more on the process via which loans by private banks create money, see this Bank of England publication, the first few sentences in particular.
As long as the NET ASSETS of the rich remains positive, they’re OK. And as for the poor, they get the extra money they want.
Of course the above explanation as to how free markets recover from recessions is not much use in the real world and because of another phenomenon pointed out by Keynes, namely the fact that wages are as he put it “sticky downwards”. I.e. given a recession, wages (particularly in the heavily unionised public sector) just DON’T FALL.
Nevertheless, it’s nice in economics to get all the theory properly worked out, and hopefully the above little bit of theory about how free markets recover from recessions is right. When it comes to dealing with economic problems of immediate practical importance, you’re on much firmer ground if you’ve got all the theory properly worked out than if you haven’t!
As with the “house and car” effect, the Pigou effect is not of any great help in the real world: i.e. it's just a point that is of theoretical interest.